Cancel common pole-zero pairs:

Cancel common pole-zero pairs that are stable:

Cancel stable pairs within a specified tolerance:

Cancel the common pole-zero pair at the origin:

Cancel common pole-zero pairs of a fourth-order system:

The common pole-zero pair is evident by factoring the transfer function:

Cancel pole-zero pairs for a discrete-time system:

Cancel pole-zero pairs for a system with input delay:

Cancel common pole-zero pairs that are stable:

Cancel pole-zero pairs with tolerance not greater than 0.01:

With zero tolerance nothing is canceled:

This system has two pole-zero pairs whose tolerance is less than or equal to 0.6:

Cancel the pair with frequency greater than 9 radians per time unit:

Visualize the responses of the three systems to a unit step input:

Use TransferFunctionCancel to obtain a simpler representation of a highly oscillatory system in a series with a notch filter:

A system of higher order is obtained without the cancellation:

In most cases the pole-zero cancellation has a negligible effect on the overall dynamics:

TransferFunctionCancel is equivalent to MinimalStateSpaceModel for SISO systems:

A system with an unstable pole-zero cancellation may appear stable:

But it is internally unstable:

TransferFunctionCancel does not support internal delays: